Vortex instabilities in three-dimensional boundary layers: the relationship between Görtler and crossflow vortices
Vortex instabilities in three-dimensional boundary layers: the relationship between Görtler and crossflow vortices
复制标题
三维边界层中的涡不稳定性：Görtler 与横流涡之间的关系
作者：
A. Bassom;P. Hall
对于可以支持 Görtler 涡流和横流涡流的边界层，解决了无粘性和粘性稳定性问题。当代表所考虑的基本边界层流的三维程度的参数增加时，发现戈特勒涡结构的变化。结果表明，随着该参数的增加，横流涡流自然出现，并最终成为流动中唯一可能的涡流不稳定性。结论表明，在横流值足够大的情况下，边界层中不存在不稳定的戈特勒涡流，在零横流情况下，边界层是离心不稳定的。结果表明，在许多实际应用中，戈特勒涡旋不能成为转变的原因，因为它们被基态的三维性质所破坏。在后掠翼流中，对于大约 20° 的典型后掠角，戈特勒机制可能不存在。对弱三维边界层中涡不稳定性的接受性问题进行了一些讨论；结果表明，无粘性模态的耦合系数略小于 Denier、Hall 和 Seddougui (1991) 最近讨论的增长最快的粘性模态的耦合系数。然而，事实上，在大多数情况下，无粘模式的增长率较大，这意味着它们可能是更有可能的转变来源。
The inviscid and viscous stability problems are addressed for a boundary layer which can support both Görtler and crossflow vortices. The change in structure of Görtler vortices is found when the parameter representing the degree of three-dimensionality of the basic boundary-layer flow under consideration is increased. It is shown that crossflow vortices emerge naturally as this parameter is increased and ultimately become the only possible vortex instability of the flow. It is shown conclusively that at sufficiently large values of the crossflow there are no unstable Görtler vortices present in a boundary layer which, in the zero-crossflow case, is centrifugally unstable. The results suggest that in many practical applications Görtler vortices cannot be a cause of transition because they are destroyed by the three-dimensional nature of the basic state. In swept-wing flows the Görtler mechanism is probably not present for typical angles of sweep of about 20°. Some discussion of the receptivity problem for vortex instabilities in weakly three-dimensional boundary layers is given; it is shown that inviscid modes have a coupling coefficient marginally smaller than those of the fastest growing viscous modes discussed recently by Denier, Hall & Seddougui (1991). However, the fact that the growth rates of the inviscid modes are the larger in most situations means that they are probably the more likely source of transition.